A moving bump in a continuous manifold: a comprehensive study of the tracking dynamics of continuous attractor neural networks

Neural Computation
C C Alan FungSi Wu

Abstract

Understanding how the dynamics of a neural network is shaped by the network structure and, consequently, how the network structure facilitates the functions implemented by the neural system is at the core of using mathematical models to elucidate brain functions. This study investigates the tracking dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of neuronal recurrent interactions, CANNs can hold a continuous family of stationary states. They form a continuous manifold in which the neural system is neutrally stable. We systematically explore how this property facilitates the tracking performance of a CANN, which is believed to have clear correspondence with brain functions. By using the wave functions of the quantum harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is decomposed into different motion modes, corresponding to distortions in the amplitude, position, width, or skewness of the network state. We then develop a perturbation approach that utilizes the dominating movement of the network's stationary states in the state space. This method allows us to approximate the network dynamics up to an arbitrary accuracy depending on the order of perturbation ...Continue Reading

References

Feb 1, 1989·Journal of Neurophysiology·S FunahashiP S Goldman-Rakic
Jan 1, 1972·Biophysical Journal·H R Wilson, J D Cowan
May 1, 1984·Proceedings of the National Academy of Sciences of the United States of America·J J Hopfield
Apr 25, 1995·Proceedings of the National Academy of Sciences of the United States of America·R Ben-YishaiH Sompolinsky
Aug 20, 1993·Science·M A Wilson, B L McNaughton
Apr 2, 1993·Science·A P GeorgopoulosA Lukashin
Nov 12, 1996·Proceedings of the National Academy of Sciences of the United States of America·H S Seung
Jan 7, 1999·Journal of Computational Neuroscience·M Camperi, X J Wang
Apr 7, 1999·Nature·M J BerryM Meister
Jul 21, 1999·Nature Neuroscience·S DeneveA Pouget
Jul 7, 2001·Neural Computation·C R Laing, C C Chow
Jul 31, 2001·Trends in Neurosciences·X J Wang
Apr 26, 2002·Neural Computation·Si WuHiroyuki Nakahara
Jun 14, 2002·Network : Computation in Neural Systems·S M StringerI E T de Araujo
Nov 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xiaohui XieH Sebastian Seung
May 17, 2003·Biological cybernetics·Wolfram Erlhagen
Jan 13, 2004·Reviews in Medical Virology·P D Griffiths
Feb 10, 2004·Journal of Physiology, Paris·Boris GutkinBard Ermentrout
Aug 18, 2005·Neural Computation·Si Wu, Shun-ichi Amari
Dec 16, 2005·Neural Computation·Arnulf B A GrafBernhard Schölkopf
Aug 10, 2006·Journal of Vision·Jan JastorffMartin A Giese
Dec 1, 2007·Neural Computation·Christian K Machens, Carlos D Brody
Dec 19, 2007·Neural Computation·Si WuShun-Ichi Amari
Jan 1, 1995·IEEE Transactions on Neural Networks·R L Fry

❮ Previous
Next ❯

Citations

Oct 11, 2012·Proceedings of the National Academy of Sciences of the United States of America·Yoram Burak, Ila R Fiete
Mar 21, 2012·Neural Computation·Wenhao Zhang, Si Wu
May 15, 2013·Neural Computation·Hongzhi You, Da-Hui Wang
Apr 18, 2013·PLoS Computational Biology·Dominic StandageMichael C Dorris
Feb 9, 2011·Neural Computation·Yao LuShun-Ichi Amari
Jul 3, 2010·Science China. Life Sciences·Si Wu, PeiJi Liang
Jan 21, 2015·Neural Computation·C C Alan Fung, S-i Amari
Sep 30, 2016·Frontiers in Computational Neuroscience·Yuanyuan MiSi Wu
Apr 20, 2019·PLoS Computational Biology·Alexander SeeholzerWulfram Gerstner
Oct 16, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·He WangSi Wu
Sep 19, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C C Alan FungSi Wu
Dec 7, 2018·Frontiers in Neuroscience·Lei DengYuan Xie
Apr 24, 2019·Physical Review Letters·Chi Chung Alan Fung, Tomoki Fukai
Sep 15, 2021·ELife·Davide SpallaAlessandro Treves
Nov 16, 2021·Frontiers in Computational Neuroscience·Leijun Ye, Chunhe Li

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.